NTA JEE Main 7th April 2013 Online

An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross-sectional area A. When the piston is in equilibrium, the volume of the gas is $$V_0$$ and its pressure is $$M_0$$. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[Assume the system is in space.]

A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are $$7.7 \times 10^3$$ kg m$$^{-3}$$ and $$2.2 \times 10^{11}$$ N m$$^{-2}$$ respectively?

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is :

In an LCR circuit shown below, both the switches are open initially. Now switch $$S_1$$ is closed, $$S_2$$ kept open. (q is charge on the capacitor and $$\tau$$ = RC is capacitive time constant). Which of the following statement is correct?

Two capacitors $$C_1$$ and $$C_2$$ are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then:

The supply voltage to a room is 120 V. The resistance of the lead wires is 6 $$\Omega$$. A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb?

This question has Statement I and Statement II. Of the four choices given after the Statements, choose the one that best describes the two Statements.
Statement - I : Higher the range, greater is the resistance of ammeter.
Statement - II : To increase the range of ammeter, additional shunt needs to be used across it.

Two short bar magnets of length 1 cm each have magnetic moments 1.20 A m$$^2$$ and 1.00 A m$$^2$$ respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the south. They have a common magnetic equator and are separated by a distance of 20.0 cm. The value of the resultant horizontal magnetic induction at the mid-point O of the line joining their centres is close to
(Horizontal component of earth's magnetic induction is $$3.6 \times 10^{-5}$$ Wb m$$^{-2}$$)

A metallic rod of length $$l$$ is tied to a string of length $$2l$$ and made to rotate with angular speed $$\omega$$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is:

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with a bigger loop is: